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Polarization properties and energy stability are measured for few-cycle pulses that are generated by filamentation in dual Ar-filled tubes in tandem. The dual-tube geometry enhances the contribution of self-phase modulation to spectral broadening. The polarization extinction ratio (I⊥/I‖) is improved for the beam transmitted through the second tube compared to the first tube and of the incident laser beam. Polarization control of few-cycle pulses is realized in simple fashion by a half-wave plate placed prior to the dual-tube assembly. We show that intensity clamping in the filament affords a major advantage in accomplishing a significant reduction in energy fluctuations compared to those inherent in the incident laser beam.
©2008 Optical Society of America
1. Introduction
Intense few-cycle optical pulses have achieved considerable significance in the contemporary pursuit of attosecond pulses and in studies of light-matter interactions in the strong field regime [1]. Different strategies for few-cycle pulse generation have been adapted, such as hollow-fiber pulse (HFP) compression [2] and optical parametric amplification [3]. HFP methods are the most widely adopted in spite of practical limitations like low coupling efficiency and alignment difficulties. Recently, a simple method based on filamentation in gas has been introduced to generate few-cycle pulses [4–8]. 5 fs carrier envelope offset phase stable pulses have been generated employing two stage filamentation in argon [5]. Indeed, it has also been predicted that the single-cycle limit might be accessible using filamentation in a gas tube [9–13].
Filamentation occurs when an ultrashort pulse with sufficient power propagates in a transparent medium [14–16]. The consequent self-guiding experienced by the propagating beam gives rise to spatial filtering, resulting in excellent beam quality. Two mechanisms dominate filamentation dynamics: the optical Kerr effect and multiphoton ionization (MPI). The former gives rise to self-focusing of the beam and the latter results in plasma formation that leads to defocusing and it is the dynamic balance between the two that limits the intensity inside the filament [17]. This clamped intensity is ~1013 W cm-2 for filamentation in air [18]. At this intensity air molecules ionize: a weak, underdense plasma is formed. With plasma density as low as 1016 cm-3 insignificant amounts of laser energy are absorbed, and the resulting electron distribution is homogeneous enough to ensure that the intensity and fluence distribution inside the filament remains unaffected [16]. Each filament may be thought of as being a superposition of two contributors: one is the core or fundamental mode that is intense and has improved spatial mode quality [19], and the other is from background, higher-order spatial modes that have larger diameter and are less intense.
From the viewpoint of few-cycle pulse compression, some comparisons of filamentation and HFP methods have been made [20,21] which have focused on parameters like pointing stability, spectral properties, and spatial chirp. The beam pointing stability achieved in both methods appears comparable and depends on gas pressure. HFP compression yields nearly flat-top spectra, due to self phase modulation (SPM). On the other hand, the blue-side component of the spectrum that is obtained upon filamentation compression is enhanced due to contributions by free-electron-induced SPM. Recently, supercontinuum generation has been reported in the wavelength range 200–1000 nm by focusing a 45 fs, 805 nm laser pulse into two Ar gas filled tubes in tandem [22] such that the first cell yields a broad spectrum that is temporally compressed and then focused into a second tube to generate an even broader spectrum that is again temporally compressed using chirped dielectric mirrors (CDMs).
For efficient pulse compression the polarization of the broadened spectrum must be linear [23]. In earlier studies in isotropic media [24] it was observed that, at relatively low power levels, the polarization of the generated supercontinuum is the same as that of the incident laser pulses; hence, by using a simple half-wave plate or quarter-wave plate it ought to be possible to change the polarization of the supercontinuum. Further, with increase in incident laser power it has been observed that the extinction ratio of the supercontinuum is degraded after the onset of MPI-induced free electron generation [25] and on formation of multiple filaments that induce local anisotropy in the refractive index [26]. As noted above, filamentation-based generation of few-cycle pulses (FCP) involves an under-dense plasma. It therefore becomes important to investigate the polarization properties of filamentation-based FCP and this constitutes the main driver for the present study.
Here, we investigate the polarization properties of the supercontinuum that is generated during filamentation in Ar gas by measuring its extinction ratio, i.e. the ratio of transmitted intensity I⊥ when the analyzer is in cross position to that of transmitted intensity I‖ when it is parallel, at various values of gas pressure. ER is a useful parameter to quantify the extent of cross coupling of polarization due to non-uniformities in a medium. We show that the plane of polarization of FCPs can be readily and simply altered. Further, we investigate spectral broadening in our dual-cell geometry in detail. We also report here results pertaining to energy stability of the filamentation-based scheme of few-cycle pulse generation. We show that intensity clamping in the filament affords a major advantage in accomplishing a significant reduction in energy fluctuations compared to those inherent in the incident laser beam even when the incident power, Pin is barely twice Pcr, the critical power for self-focusing. Improvement in the energy stability due to intensity clamping has been recently observed in four wave mixing and third harmonic generation experiments during the filamentation in gases [17].
2. Experimental details
Few-cycle pulses are generated using incident light from a Ti-sapphire laser (0.45 mJ, 50 fs pulses centered at 800 nm) at 1 kHz repetition rate. A schematic depiction of our apparatus is shown in Fig. 1. After passing through an aperture (4 mm) the laser beam (0.4 mJ) was focused with a 1 m focal length metal-coated spherical mirror on to a 1.5 m long tube filled with Ar gas (tube 1). The central part of the output beam (0.23 mJ) containing the supercontinuum was extracted by passing the beam through a 3 mm aperture. The thicknesses of the entrance and exit fused silica windows were 300 µm.
Light pulses traversed though a total air path of 2 m before being incident on CDM1 (BBCOMP, Femtolasers) wherein compression to 16 fs pulses was achieved (chirp compensation ~-150 fs2 at 800 nm). These compressed pulses traversed though 0.5 m of air path before being focused by M4 on to a second, 1 m long tube filled with Ar (tube 2).
The central part of the resulting supercontinuum was sampled by a 3 mm aperture and was compressed (total air path of 3 m) using CDM2 and M6 (chirp compensation ~-180 fs2 at 800 nm). The compressed pulses were characterized by means of spectral phase interferometry for direct electric field reconstruction, SPIDER (Avoca-7 Del Mar).
We measured the extinction ratio, ER (=I⊥/I‖), of the incident laser pulse and the supercontinuum using an uncoated Glan-Thompson polarizer (ER=10-5) covering the wavelength range 350–2200 nm. The energy of the supercontinuum after the analyzer was measured using a photodiode (wavelength range of 430 to 1100 nm) coupled to an integrating sphere and its spectrum was recorded using a fibreoptic-coupled spectrometer (Ocean Optics, Model USB 4000).
Fig. 1. Experimental setup for generation of few-cycle pulses by filamentation in two Ar-filled tubes in tandem. M1 is a plane mirror. M2–M5 are concave mirrors of focal length 1m. CDM1, CDM2, and M6 are chirped dielectric mirrors. A1–A3 are apertures.
3. Results and discussion
We have probed how spectral broadening depends on the pressure of Ar gas and have observed that as values are made sufficiently high there is a reduction in the bandwidth of the supercontinuum. The spectral profiles obtained after the first and second tubes are shown in Fig. 2.
Fig. 2. Spectral profiles of broadened light emerging from Ar-filled gas tubes 1 (red) and 2 (blue). The spectral profile of the incident laser beam (black) is also shown.
The pressure in the first tube was kept at 1.2 atm while in the second tube it was 0.9 atm of Ar. These spectra were recorded after CDM1 and CDM2, respectively. Each set of chirped mirrors covered the wavelength range 650–900 nm. The broadening around 800 nm is more after the second tube, indicating that the SPM contribution becomes significantly enhanced compared to the first tube. This can be understood from the fact that self phase modulation depends on the time-varying intensity; hence a shorter pulse (16 fs) produces greater broadening compared to a 50 fs pulse. Recently, Akozbek, et al., [20] have measured continuum that extends beyond 250 nm using 10 fs and 6 fs pulses. The observed spectra were modeled taking into account self-steepening along with self phase modulation.
In measurements that we report in the following, the pressure in the first tube was again kept at 1.2 atm while the second tube was filled with 0.9 atm of Ar. The incident power in the first tube and the second tube was less than 2Pc (we estimate Pcr for Ar to be 6 GW at 1.2 atm and 8 GW at 0.9 atm [27]). These values ensured that we operated in the single-filament regime in both the tubes. Further confirmation of the single-filament regime was obtained by measuring the spatial beam profile and transmittance of the self focused beam through an aperture [28]. Figure 3 shows a typical SPIDER trace and corresponding spectrum after final compression achieved using a pair of chirped dielectric mirrors. Note that the pulse duration is measured to be ~10 fs and we observe essentially flat and zero phase. The energy of our 10 fs pulse was ~0.2 mJ with incident energy of 0.45 mJ for 50 fs pulses, giving an overall total efficiency of nearly 40%.
Fig. 3. SPIDER traces of the compressed laser pulse emerging from tube 2 showing a) the temporal profile, and b) the spectral profile. The pressure in the first tube was kept at 1.2 atm while in the second tube it was 0.9 atm of Ar.
We now discuss the measurements pertaining to polarization extinction ratio of the supercontinuum generated in tube 1 and tube 2. All measurements of ER were performed by setting the wavelength at 800 nm in the energy meter. The extinction ratio (I⊥/I‖) of the incident laser pulse was measured to be 1.5×10-3.
Figure 4 shows the variation of ER of the generated supercontinuum from tube 1 and tube 2 as a function of Ar gas pressure at fixed incident laser energy of 0.4 mJ, using incident pulses of 50 fs duration. The ER of the supercontinuum from tube 1 exhibits a 20% improvement compared to the ER associated with the incident laser light at 1 atm gas pressure. Further, the ER value remains more or less constant even at 1.2 atm argon pressure. It is only at pressures beyond 1.4 atm that the ER value degrades, by ~20% as compared to that of the incident laser. With Ar pressure in tube 1 maintained at 1 atm and energy incident on tube 2 fixed (0.24 mJ, 16 fs), the ER of the supercontinuum from tube 2 was measured as a function of Ar pressure in tube 2. At a pressure of 0.6 atm the ER of the supercontinuum after tube 2 is seen to improve by ~20% as compared to that after the first tube. Even at 0.9 atm the ER value remains better than that of the incident beam from tube 1. In the pressure range 1.4–2.0 atm pressure there is marginal change in ER values. Thus, the ER value of tube 2 shows improvement by 20% as compared to tube 1, and by as much as 50% compared to ER values associated with the incident laser.
Fig. 4. Extinction ratio plotted as a function of argon pressure in a) tube 1 and b) tube 2. The solid lines are simply a guide to the eye.
Fig. 5. Spatial profile of a) the incident laser beam and b) the beam after spatial self-cleaning in filamentation (diameter is 2mm at 1/e2).
Figures 5(a) and 5(b) show the images of the beam profile of the incident laser and the filament core (from tube 2) that we measured using a CCD camera based beam profiler. The improvement in ER that is depicted in Fig. 4 can thus be attributed to the overall improvement in the spatial mode quality of the beam undergoing filamentation in our dual-tube geometry.
We introduced a half-wave plate in the incident laser path before the gas tubes and observed that the plane of polarization of the FCP could be readily rotated, that is, from horizontal to vertical and vice-versa. On introducing a quarter-wave plate we generated a circularly polarized supercontinuum after tube 1.
To probe the energy stability of our filamentation-generated few-cycle pulses we simultaneously monitored time-elapsed energy fluctuations from the incident laser, tube 1 (argon pressure 1.2 atm) and tube 2 (argon pressure 0.9 atm) using fast photodiodes (DET 210, Thor Labs) coupled to a digital oscilloscope; data are depicted in Fig. 5 as normalized energy variations over time, and show reduction of rms fluctuations from 3.3% to 1.8% after two stages of filamentation.
We discuss the observed energy fluctuations of generated supercontinuum during filamentation. SPM, of course, scales nonlinearly with incident laser intensity (see, for instance, [29]). The broadband intensity after the first tube should, therefore, exhibit much larger fluctuations in the absence of any saturating mechanism. However, our measurements clearly reveal that the broadband intensity after tube 1 exhibits lower energy fluctuation than that of incident laser due to the intensity clamping. To be quantitative, we measure the rms fluctuation to be 2.4% after tube 1 and 1.8% after tube 2. Further, the reduction in energy fluctuation after each tube is nearly the same (~25%), with the overall reduction being ~45%, thus substantially improving the energy stability of the FCP in a dual tube configuration.
Fig. 6. Energy fluctuations as a function of time, note the 45% reduction in fluctuations after tube 2 with respect to the laser.
In summary, we have demonstrated an improvement in the polarization extinction ratio of the supercontinuum that is generated during filamentation in dual argon-filled gas tubes in tandem as compared to the extinction ratio of the incident laser beam. Direct imaging of the laser beam enables us to attribute this to significant improvement in the spatial mode quality brought about by filamentation. Furthermore, we have discovered that with increase in the gas pressure beyond about 1.4 atm in our tubes, a little degradation of the extinction ratio is seen to occur. The smallness of this is an indication of the robustness of the filamentation process. On the other hand, the small change in ER that is detectable may possibly be brought about by non-uniformities in the electron density in the plasma. Detailed modeling of such plasma effects will have to be carried out in order to develop better insights and to probe how ER effects scale at incident energies. Such modeling remains a challenge. We also show that by using a half-wave plate placed prior to the dual-tube assembly we can control the plane of polarization of the few-cycle pulses that we generate. Finally, we have shown that due to intensity clamping, we observe significant improvement of energy stability in filamentation based few-cycle pulse generation. Taken together both these facets are of considerable importance in application of this method of generating few-cycle pulses to studies of strong-field molecular dynamics in the ultrashort temporal domain and some preliminary work has already been carried out in which 10 fs pulses of intense light have been used by us to probe the ionization and dissociation of molecules like CS2 and H2O [30, 31].
Acknowledgment
We acknowledge partial financial support from the Department of Science and Technology. Useful technical discussions on SPIDER with Catherine Kealhofer (Stanford University) are gratefully acknowledged.
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